Efficient method for mapping a logic design on field programmable gate arrays

ABSTRACT

An efficient method for mapping a logic design on Field Programmable Gate Arrays involves a determination of the minimum required square grid of FPGA logic blocks for mapping the design, providing a compensation factor on the minimum square grids, selecting the maximum value among the compensated square grids for reducing the mapping time; and implementing a legalization adjustment to ensure mapping of said compensated design.

RELATED APPLICATION

The present application claims priority of India Patent Application No 2595/Del/2004 filed Dec. 29, 2004, which is incorporated herein in its entirety by this reference.

FIELD OF THE INVENTION

The present invention relates to an efficient method for mapping a logic design on Field Programmable Gate Arrays.

BACKGROUND OF THE INVENTION

Field Programmable Gate Arrays (FPGAs) are configurable logic devices, which are used to implement varied logic functions. The basic FPGA consists of Look Up Tables (LUTs) and routing paths but a complex one includes dedicated RAM, logic/I/O blocks and other macros like adders, multipliers etc. These FPGAs can be configured to produce a desired output by interconnecting said blocks through routing paths. This process of implementing logic of a design on a FPGA by interconnecting configurable logic devices is known as FPGA mapping. Since being first introduced by XILINX in 1985, the FPGAs have become increasingly popular devices for use in electronics systems. The use of FPGAs continues to grow exponentially because they offer relatively short design cycles, with huge reduction in costs through logic consolidation, and flexibility in terms of configurability.

Several FPGA placement systems have been developed to optimally implement the desired designs on a FPGA. The systems try to map the desired designs onto a grid of configurable logic blocks on a FPGA device of particular size. The net-list for the design, and the Input/Output pad (I/O pad) information of the chip are given as the inputs to the placement system and the system outputs the coordinates for each mapped logic element on a FPGA and interconnection information for logic elements. Over the last few decades, the FPGA placement problem has been solved by various techniques like analytic, partition based and Simulated Annealing. Two parameters of design cycle i.e., delay time and required Silicon area are optimized to get the best possible results. These systems also consider the mapping time and routability of the placed design while mapping the design on a FPGA.

Out of all techniques mentioned here, most FPGA placement systems are based on a variant of Simulated Annealing (SA) as SA usually results in most optimal solution in terms of silicon area and delay time. SA is a Monte Carlo approach for minimizing multivariate functions. The parameter involved in the case of placement is the cost of the placement in terms of wire length or some other factor. The temperature T is a parameter that controls the likelihood of accepting moves that makes the placement worse.

Initially T is very high so almost all moves are accepted. It is then gradually decreased, as the placement is refined so that eventually the probability of accepting moves that makes the placement worse is very low. To apply SA, the system is initialised with a particular random placement. A new placement is constructed by random displacement of the configurable logic devices. If the cost of this new state is lower than that of the previous one, the change is accepted unconditionally and the placement is updated. If the energy is greater, the new placement is accepted probabilistically. This is the Metropolis step, the fundamental procedure of SA. This procedure allows the system to move consistently towards lower cost, yet still ‘jump’ out of local minima due to the probabilistic acceptance of some upward moves.

While various FPGA configurations are currently used, the FPGA devices mentioned herein represent a square grid of configurable elements on a FPGA. For example, a FPGA with device size 17 represents a FPGA having a square grid of configurable logic blocks with 17 rows and 17 columns and routing paths in between. The square arrangement helps in ensuring minimization of wire length in a design and thus reducing the placement cost.

There are two inherent problems with these SA based placement systems. Firstly, when the design size is almost equivalent to the FPGA device size, the present day systems are unable to produce an optimal FPGA placement for large designs within a reasonable amount of time. This is because there is a limited free space available for movement of logic blocks and as a result, the system performs significant amount of switching of logic blocks to find an optimal placement. The other problem is the availability of excess free space for movement of logic blocks when the design size is much smaller than the device size. The larger the device size the more number of moves SA will make and as a result, the system would take more time to find optimal placement. This is observed in FIG. 1 and FIG. 2.

The graph of FIG. 1 gives a very clear idea about the behavior of SA. XorMux8 requires a minimum of device size 17[15×15 for Logic blocks and I/O's on periphery]. The placement cost of SA is low in the region between 25 and 38. For very high device size, when the logic blocks have excess space to move, the SA produces very bad results. Moreover the deviation in the results, or in other words the randomness of SA is also increased for higher device size. The graph has been computed taking an average of mapping cost of five runs for each value of device size. If a design were to run only once for each device size, the deviation would even be larger.

The extra silicon area given to the logic blocks is to allow the SA to have more “moves” in which only a single cell is involved (i.e. no swapping) during the initial phase. This will facilitate SA to have a better intermediate solution compare to one with inappropriate silicon area.

The larger the device size the more number of moves SA will make. For more number of moves SA would take more time. But it is found that SA takes more time for less number of moves and produce a sub-optimal solution when it has very little free silicon area to move i.e. when the design size is almost equal to the device size. This is illustrated in FIG. 2.

As seen in the graph of FIG. 2, the placement time decreases till the device size is around 24 and then increases again. When the device size is near 17 [minimum size for XorMux8] the logic blocks are very tightly packed and hence the each move of SA actually involves two logic blocks (i.e. swapping). As shown in FIG. 3 and FIG. 4 below, almost all moves in FIG. 3 will involve two or more logic blocks where as moves in FIG. 4 will mostly involve one logic block.

Ideally the system should produce an optimal FPGA mapping, but the mapping time for a design adversely affects the system output. As the time passes, the parameter T decreases for SA based systems and as result, the probability of accepting a worse placement also decreases. For big designs the system may accept a sub-optimal placement, as eventually the system may not be able to accept a worse output in the proximity. Hence, eventually the system accepts a sub-optimal placement as an output if better placement is not found in the proximity. The system placement results are illustrated in terms of placement cost and placement time for various device sizes in FIGS. 1 & 2 respectively. As observed, both parameters initially decrease as the FPGA device size increases. However, the parameters start to increase, as the device size gets significantly bigger than the design size. Moreover, the deviation in the results, or in other words the randomness of the output is also increased for higher device size.

The miniaturization of semiconductor technology and increase in the number of logic elements in the present day designs has made the present FPGA mapping systems very slow and unreliable for producing feasible FPGA implementation. All existing techniques produce far from the optimal solution. The present day systems are very slow in providing optimal mapping and hence, are very undesirable for FPGA implementation of designs with large number of logic elements. To truly exploit FPGAs for rapid turn-around development and prototyping, placing of processing elements in proper locations of the device plays an important role in determining the delay and the silicon requirement for FPGA implementation of a design.

Hence, there is a need for systems that minimize the chip area and delay time for a design, and at the same time reduce the mapping time. The present invention relates to efficient FPGA placement system for designs with large number of logic elements using SA based approach. The present invention provides a placement system for efficient FPGA implementation of big designs. The Required Silicon area is dominated either by the I/O's, Logic Blocks or Macro Height.

SUMMARY OF THE INVENTION

To obviate the drawbacks of the prior art an object of the instant invention is to provide a system that results in reduced silicon area for designs with large number of logic elements. A further object of the invention is to reduce the timing delay for the mapped design on FPGA. Another object of the invention is to reduce the time taken for mapping the above mentioned designs on a FPGA.

To achieve the above objects the instant invention provides an efficient method for mapping a logic design on Field Programmable Gate Arrays involving the steps of determining the minimum required square grid of FPGA logic blocks for mapping said design, providing a compensation factor on the minimum square grids, and selecting the maximum value amongst the compensated square grids for reducing the placement time, and implementing a legalization adjustment to ensure mapping of said compensated design. Preferably, to determine the minimum require square grid involves a determination of the minimum required number of FPGA logic blocks in a square grid for mapping corresponding design logic blocks, a determination of the minimum required number of FPGA logic blocks in a square grid for mapping corresponding design Input/Output blocks, a determination of the minimum required number of FPGA logic blocks in a square grid for mapping corresponding design macros.

In a preferred embodiment, the compensation factor for the square grid for the design logic blocks is calculated by multiplying said square grid for the design logic blocks by a factor ‘X’, the compensation factor of the square grid for the design Input/Output blocks is calculated by multiplying the number of Input/Output blocks by a factor ‘Y’, and the compensation factor for the square grid for the design macros is preferably calculated by multiplying the number of macro blocks with a factor ‘Z’. Preferably, ‘X’ ranges between 1.5 to 3, ‘Y’ is 1 when more than one I/O logic block is held in Input/Output coordinate, and ‘Y’ is 1.2 when Input/Output coordinate holds only one I/O logic block, and factor ‘Z’ is 1.2.

BRIEF DESCRIPTIONS OF THE DRAWINGS

The invention will be described with reference to the accompanying drawings.

FIG. 1 shows the graph of placement cost versus device size.

FIG. 2 shows the graph of variation of placement time with increasing device.

FIGS. 3 and 4 show the moves involving the logic blocks.

FIG. 5 shows the graph of logic block dominated design.

FIG. 6 shows the graph of I/O or macro dominated design.

FIGS. 7 and 8 show the device sizes.

FIGS. 9 to 13 show different simulation results.

DETAILED DESCRIPTION OF THE INVENTION

To truly exploit FPGAs for rapid turn-around development and prototyping, placing of processing elements in proper locations of the device plays an important role in determining the delay and the silicon requirement for FPGA implementation of a design. The present invention provides a mapping system for efficient FPGA implementation of big designs. Based on the analysis in background, the mapping system determines the appropriate FPGA device size to place a design.

The Required Silicon area for each case is determined the following way.

-   -   a) L=Required Silicon area for Logic Blocks=Square Root (Number         of Logic Blocks).     -   b) I=Required Silicon area for I/O's=I=(Number of I/O Cells         required)/2.     -   c) M=Required Silicon area for Macros=max (Maximum Height of         Macro, Maximum Width of Macro).

To get the optimal required silicon area we characterize the behavior of the above three categories of designs. For Logic Block dominated designs with small difference between L and I, the behavior is as shown in FIG. 5. For I/O dominated designs having huge difference between L and I, the behavior is as shown in FIG. 6. For Macro dominated designs also the behavior is as shown in FIG. 6 for designs where the difference between L and I is huge and similar to FIG. 5 where the difference between L and I is small.

In cases where the difference between L and I is small for I/O dominated designs or L and M is small for Macro dominated designs, the behavior is similar to FIG. 5 because in such cases the values of I or M lie in region A of FIG. 5. In other words the Logic Blocks are still tightly packed due the small difference between L and I for I/O dominated designs or L and M for Macro dominated designs. Hence the logic blocks do not get enough free space to move.

Therefore for all designs the target should be to achieve Region B. However due to the minimum space required for I/O dominated designs or Macro dominated designs, the device size in region B may not be sufficient to place all I/O's or satisfy the macro heights. In such a scenario a value in region C is chosen (the behavior in region C is similar to FIG. 6). Another parameter that plays an important role in choosing the optimal device size is the placement time. It is evident from FIG. 1 and FIG. 2 that the time increases in the second half of the region B. To get the optimal value of required silicon we compute the value of L, I and M according to the following procedure:

-   -   A) Computing Value of L_(m)         -   L_(m)=L*w, where the factor w can be in the range of 1.5 to             3.     -   B) Computing Value M_(m)         -   Twenty percent extra silicon area is given to Macros.         -   Hence M_(m)=M*1.20     -   C) Computing Value of I_(m)         -   The computation of I depends on the architecture of the             device.         -   i) If a single I/O co-ordinate can hold more than one I/O,             then I is not to be modified         -   ii) If a single I/O co-ordinate holds only one I/O then             twenty percent extra silicon area is given.         -   Hence I_(m)=I*1.2.

The maximum value amongst the computed values of L_(m), I_(m) and M_(m) is taken and set as the required silicon area for the design. Hence, Required Silicon for design=Rm=Max (L_(m), I_(m), M_(m))

The extra silicon area given to the logic blocks is to allow the SA to have more “moves” in which only a single cell is involved (i.e. no swapping) during the initial phase. This will facilitate SA to have a better intermediate solution compare to one with inappropriate silicon area.

Re-Adjustment of Rm

The required silicon area Rm calculated may not be sufficient to place all macros. Also the I_(m) value takes only two sides I/O mapping into account. The I/O mapping on the other two sides is not calculated. Hence some adjustments are done to require silicon value (Rm). The following two steps are further carried out to find the

-   -   1) A legalization algorithm is executed to find the minimum         amount of device required to place all the macros without         legalization.         -   Hence ML=Legalization Value for macros.     -   2) The I_(m) value is readjusted as I_(Final)=Min         (I_(m, Device size)). This is done to allow I/O's to use all the         four sides of the device if the I_(m) value exceeds the device         size.         -   Hence, Final Required Silicon for design=RS=Maximum (R_(m),             ML, I_(final))

The required Silicon Area can exceed the device size. The SA apparatus would usually converge itself in such cases to an area supported by the device size. A post placement method may be required to set the logic block co-ordinates to valid co-ordinates with respect to the device size as shown in FIG. 7 and FIG. 8 below. As shown in FIG. 7 the placed design has co-ordinates from 0 to RS. Hence the entire placement needs to be shifted as shown in FIG. 8.

An example when a design may consume a larger area than the amount required by it is shown below. For example an area of 8×8 may be sufficient for a design fed to an SA based placer. But the SA initially maps it to the entire available chip area and then searches for the global optima in the entire device. This is demonstrated in the FIG. 9.

To overcome the problem outlined in FIG. 9 SA is prevented from using an area more than the calculated required silicon area as shown in FIG. 10. A large portion of silicon is not explored due to the restrictions set by the required silicon. This helps in reducing the placement time and produces a near optimal solution as only the required silicon area is explored. Moreover, the maximum deviation in the output of the SA apparatus is less than the output generated using the require silicon area concept. Hence randomness of SA is also decreased.

As illustrated in the FIG. 11 the I/O spread them in the design and then the SA gets trapped in local minima yielding a result very far from the optimal. Using RS in the FIG. 12 the solution space is restricted and a solution closer to the global optima is obtained.

The idea of providing more silicon area virtually is very fruitful for these designs similar to the ones shown in FIG. 13. In these designs during the annealing there are a number of moves in which two cells are swapped since there is very less vacant area. To handle such designs the designs are spread over the required silicon area (virtual since it will be more than the device size) and then annealing is started. The free silicon area will increase the number of moves in which only one cell is involved during the initial passes thus yielding a high quality intermediate solution.

Thus the aforesaid invention offers lot of advantages over the prior art. Due to bad placement of very large designs the router may not be able to route the design on a given device. Our reduced silicon area approach can map a big design in a much better way. Hence it may map even those designs that are not mapped by SA without reduced silicon on the same device. The placement apparatus searches only the appropriate solution space applicable for the design. Hence unnecessary solution space is not explored. The present invention provides following benefits over the existing method:

-   -   Reduction in randomness of SA.     -   Reduction in mapping time.     -   Preventing SA from getting trapped in local minima resulting in         wastage of Silicon area.

Further, since only the required area of silicon is used for a design, it assists in:

-   -   Reduction in the number of routing resources required.     -   Reduction in the delay in the design.     -   Reduction in the routing execution time.

Since the silicon area is restricted, the maximum deviation of the results is also decreased. Thus, the consistency of the invention is increased, as further illustrated in the tables listed below: TABLE I Calculation of RS Design I/O RLB Macro L I M

abt 100 16 0 4 25 0

add8 28 7 1 3 7 5

add16 52 13 1 4 13 9

add32 100 25 1 5 25 17

addrgen 94 154 4 13 24 17

booth 26 50 2 8 7 4

ciu_alua 119 119 0 11 30 0

de_interleaver 196 100 0 10 49 0

decoder128 135 36 0 6 34 0

FFT_butterfly 240 192 8 14 60 8

FFT_sm1 17 67 0 9 5 0

iso_main 175 109 0 11 44 0

XorMux8 54 204 0 15 14 0

XorMux16 80 408 0 21 20 0

In prior art, the FPGA device size used to map a design is 34 which uses a 34×34 size FPGA array as an initial square arrangement for the mapping systems, while Table 1 shows the required FPGA device size determined using the instant invention for initial mapping. If the value of I exceeds 34, then I_(m) is taken as Minimum (I, device Size (34)). The value of compensation factor w is taken as 2. The placement costs for various device sizes used in the mapping system are given in Table 2. As shown in Table 2, below, the highlighted values illustrate the mapping cost for the instant invention. This clearly shows the advantage of the instant invention over the prior art in terms of placement cost.

While there have been described above the principles of the present invention in conjunction with specific components, circuitry and techniques, it is to be clearly understood that the foregoing description is made only by way of example and not as a limitation to the scope of the invention. Particularly, it is recognized that the teachings of the foregoing disclosure will suggest other modifications to those persons skilled in the relevant art. Such modifications may involve other features which are already known per se and which may be used instead of or in addition to features already described herein. Although claims have been formulated in this application to particular combinations of features, it should be understood that the scope of the disclosure herein also includes any novel feature or any novel combination of features disclosed either explicitly or implicitly or any generalization or modification thereof which would be apparent to persons skilled in the relevant art, whether or not such relates to the same invention as presently claimed in any claim and whether or not it mitigates any or all of the same technical problems as confronted by the present invention. Applicant hereby reserves the right to formulate new claims to such features and/or combinations of such features during the prosecution of the present application or of any further application derived therefrom. TABLE 2 MST COST for Various Device Sizes (Required Silicon Values in Bold) Device Size abt add8 add16 add32 addrgen booth ciu_alua de_interleaver  5 NA NA NA NA NA NA NA NA  6 NA NA NA NA NA NA NA NA  7 NA 110 NA NA NA NA NA NA  8 NA 125 NA NA NA NA NA NA  9 NA 139 NA NA NA 1106 NA NA 10 NA 142 NA NA NA 1123 NA NA 11 NA 151 NA NA NA 1217 NA NA 12 NA 140 NA NA NA 1596 NA NA 13 NA 157 360 NA NA 1499 NA NA 14 NA 168 394 NA NA 1203 NA NA 15 NA 343 419 NA NA 1245 NA NA 16 NA 182 419 NA NA 1152 NA NA 17 NA 224 440 NA NA 1195 NA NA 18 NA 221 702 NA NA 1176 NA NA 19 NA 254 469 NA NA 1086 NA NA 20 NA 187 512 NA NA 2252 NA NA 21 NA 186 536 NA NA 2840 NA NA 22 NA 226 573 NA NA 1190 NA NA 23 NA 239 1043  NA NA 1315 NA NA 24 NA 239 625 NA 2636 2783 NA NA 25 548 550 599 1465 2786 2847 NA NA 26 564 238 730 1475 2645 1198 NA NA 27 571 325 680 1502 2819 1405 NA NA 28 589 245 626 1564 7036 1492 NA NA 29 593 430 745 1630 8594 1409 NA NA 30 591 394 708 1634 2843 1261 3272 NA 31 642 239 967 1640 2647 2850 3367 NA 32 625 202 761 1716 2816 1256 3467 NA 33 618 202 775 1749 2899 4365 3747 NA 34 646 339 829 1891 9077 2936 3614 5484 35 659 282 958 1809 9195 1026 3448 5556 36 685 408 794 1972 2633 3107 3471 5658 37 711 304 867 2040 10070  1488 3492 5782 38 660 776 1669  1872 8225 1382 3622 5833 39 687 210 748 1930 9470 1299 3568 5939 40 623 266 929 2164 6727 1596 3625 6040 41 608 218 723 1881 10401  1171 3464 6015 42 628 400 702 2132 6081 1643 3474 6231 43 673 232 1056  2300 10145  4039 3731 6321 44 594 204 659 2036 12054  1548 3519 6382 45 618 519 1078  2091 3101 1724 4187 6373 46 739 253 664 2106 3311 3943 4237 6602 47 618 411 785 2793 12726  1374 3606 6588 48 735 298 1253  2150 12807  1263 3615 6752 49 634 1100  989 2678 3177 4778 3524 6572  0 687 200 1136  2343 3244 1553 3539 6877 Device Size decoder128 FFT_butterfly FFT_sm1 iso_main XorMux8 XorMux16  5 NA NA NA NA NA NA  6 NA NA NA NA NA NA  7 NA NA NA NA NA NA  8 NA NA NA NA NA NA  9 NA NA 1172 NA NA NA 10 NA NA 1155 NA NA NA 11 NA NA 1150 NA NA NA 12 NA NA 1149 NA NA NA 13 NA NA 1100 NA NA NA 14 NA NA 1090 NA NA NA 15 NA NA 1079 NA 4354 NA 16 NA NA 1032 NA 4352 NA 17 NA NA 1030 NA 4205 NA 18 NA NA 1012 NA 4148 NA 19 NA NA 1029 NA 4176 NA 20 NA NA 1007 NA 4107 NA 21 NA NA 1021 NA 4140 8912 22 NA NA 1010 NA 4039 8891 23 NA NA 1023 NA 3977 8988 24 NA NA 1012 NA 4008 8826 25 NA NA 1027 NA 3973 8589 26 NA NA 1026 NA 3846 8467 27 NA NA 1014 NA 3932 8343 28 NA NA 1042 NA 3973 8259 29 NA NA 1002 NA 3901 8139 30 NA NA 1017 NA 3820 8221 31 NA NA 1034 NA 3880 8020 32 NA NA 1021 NA 3785 7973 33 NA NA 1009 NA 3768 8080 34 875  9990 1006 4301 3872 8036 35 906 11710 1016 4525 3886 7862 36 905 11990 1046 4553 3908 7841 37 923 12255 1010 4715 3794 7848 38 973 11260 1053 4541 3791 8029 39 936 13317 1013 4766 3825 7808 40 983 12234 1005 4931 3770 8012 41 984 13006 1064 4944 3867 7828 42 987 13499 1001 4689 4122 7678 43 1036  13062 1007 5233 3996 7698 44 1045  11920 1018 5111 3704 7694 45 1013  11766 1043 5249 3767 7787 46 1017  10750 1002 4934 3804 7840 47 1051  11836 1008 4964 3765 7787 48 1110  11385 1071 5363 3763 7870 49 1148  12798 1039 5318 3872 8085  0 1124  13002 1044 5008 3901 8062 

1. An efficient method for mapping a logic design on Field Programmable Gate Arrays comprising: determining the minimum required square grid of FPGA logic blocks for mapping said design; providing a compensation factor on said minimum square grids, and selecting the maximum value amongst said compensated square grids for reducing the placement time; and implementing a legalization adjustment to ensure mapping of said compensated design.
 2. The efficient method for mapping a logic design on Field Programmable Gate Arrays as claimed in claim 1 wherein said determining comprises: determining the minimum required number of FPGA logic blocks in a square grid for mapping corresponding design logic blocks; determining the minimum required number of FPGA logic blocks in a square grid for mapping corresponding design Input/Output blocks; and determining the minimum required number of FPGA logic blocks in a square grid for mapping corresponding design macros.
 3. The efficient method for mapping a logic design on Field Programmable Gate Arrays as claimed in claim 1 wherein said compensation factor for said square grid for said design logic blocks is calculated by multiplying said square grid for said design logic blocks by a factor ‘X’.
 4. The efficient method for mapping a logic design on Field Programmable Gate Arrays as claimed in claim 1 wherein said compensation factor of said square grid for said design Input/Output blocks is calculated by multiplying the number of Input/Output blocks with a factor ‘Y’.
 5. The efficient method for mapping a logic design on Field Programmable Gate Arrays as claimed in claim 1 wherein said compensation factor of said square grid for said design macros is calculated by multiplying the number of macro blocks with a factor ‘Z’.
 6. The efficient method for mapping a logic design on Field Programmable Gate Arrays as claimed in claim 3 wherein said factor ‘X’ ranges between 1.5 to
 3. 7. The efficient method for mapping a logic design on Field Programmable Gate Arrays as claimed in claim 4 wherein said factor ‘Y’ is 1 when more than one I/O logic block is held in Input/Output coordinate.
 8. The efficient method for mapping a logic design on Field Programmable Gate Arrays as claimed in claim 4 wherein said factor ‘Y’ is 1.2 when Input/Output coordinate holds only one I/O logic block.
 9. The efficient method for mapping a logic design on Field Programmable Gate Arrays as claimed in claim 5 wherein said factor ‘Z’ is 1.2. 